The role of the condensate in the existence of phonons and rotons

Interpretations of the characteristic phonon-roton excitations in superfluid⁴He are discussed to assess the role of the condensate. In the celebrated Landau, Feynman, Feenberg and subsequent Correlated Basic Function methods, the phonon-roton excitations are interpreted as collective density excitations. This picture, suitably modified at higher Q to take account of the correlated motion of neighbors (backflow), provides our best description of neutron scattering data at low temperature. The condensate does not play an explicit role. In the Field Theory, second quantized formulation of Bogoliubov, Hugenholtz and Pines, Gavoret and Nozières and the subsequent Dielectric Function formulation, the condensate plays an explicit role. Because of the condensate, both regular density (particle-hole) and single particle excitations contribute to the density response. The regular density (two-particle) and single particle excitations mix as particles scatter into and out of the condensate. This Density-Quasiparticle picture provides a good description of the temperature dependence of neutron scattering data. From this description, the phonon at low Q is interpreted as a joint density/quasiparticle mode strongly coupled via the condensate. At higher Q, the sharp maxon-roton is interpreted as a quasiparticle excitation less strongly coupled into the density. The sharp maxon-roton peak is a unique feature of the condensate and could not be observed in S(Q, ω) without a condensate.